Names of Polynomials

Date: 05/22/99 at 15:59:52
From: Rohan
Subject: Why is an equation having only two roots, one of which is
raised to 2, called a "quadratic equation"?
QUAD means four. But why is an equation having ONLY TWO ROOTS, one of
which is raised to 2, called a "QUADRATIC EQUATION"?
For example: - ax^2 + bx + c

Date: 05/22/99 at 20:40:32
From: Doctor Peterson
Subject: Re: Why is an equation having only two roots, one of which is
raised to 2, called a "quadratic equation"?
Hi, Rohan.
People often wonder about the word "quadratic," because they know that
"quad" usually means "four," yet quadratic equations involve the
second power, not the fourth. But there's another dimension to the
word.
Although in Latin the prefix "quadri" means four, the word "quadrus"
means a square (because it has four sides) and "quadratus" means
"squared." We get several other words from this: "quadrille," meaning
a square dance; "quadrature," meaning constructing a square of a
certain area; and even "square" (through French).
Quadratic equations originally came up in connection with geometric
problems involving squares, and of course the second power is also
called a "square," which accounts for the name. The third-degree
equation is similarly called a "cubic," based on the shape of a third
power. Then when higher-degree equations began to be studied, the
names for them were formed differently, based on degree rather than
shape (since the Romans had no words for higher-dimensional shapes),
giving us the quartic, quintic, and so on. In fact, quartic came
along later; originally a fourth degree equation was called
"biquadratic," meaning "doubly squared," which mixes the two concepts
and is doubly confusing.
So here's a table of names for polynomials and their sources:
degree name shape dimension
------ --------- ------ ---------
1 linear line (1)
2 quadratic square (2)
3 cubic cube (3)
4 quartic - 4
5 quintic - 5
You may be interested in a discussion of this question in the archives
of the math-history discussion group:
http://mathforum.org/kb/message.jspa?messageID=1376346
- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/